The purpose of this project is to develop methodology for analyzing molecular population genetics data. Work has focused on the use of nonparametric methods for localizing susceptibility loci for complex diseases in humans. Permutation based statistical tests were developed to maximize the use of the computer and reduce the dependency on asymptotic theory. One study considered the behavior of transmission disequilibrium (TDT) type statistics for multiple alle markers. Three competing statistics that have been proposed in the literature were studied, and the most powerful one was identified. A simple way of estimating the power of this test from case-control data was demonstrated. These results will help with design issues such as sample size and choosing a marker system. Since TDT tests only work in the presence of linkage disequilibrium, it is common to first do a case- control study to identify population association, and then do a TDT test to test the hypothesis that the association is due to linkage. Very often these two tests use the same case data, thereby creating a correlation that inflates the power of the test as well as the Type 1 error. Using permutation methods the proper way to carry out this procedure in order to guarantee the nominal significance level was identified. A common strategy for analyzing multiallele marker data is to collapse the data into two categories and proceed as if the marker has just two alleles. In light of previous results, there is no longer any need to collapse the data, unless collapsing could lead to a more powerful test. A method was developed to identify the most powerful collapsing strategy, and its statistical properties examined. Permutation methods in quantitative genetics are also under study. A permutation based procedure that considers all markers on a chromosome simultaneously was developed. This approach deals effectively with the multiple testing issue. The procedure compared favorably to one recently proposed by Kruglyak and Lander, and in some instances was found to be more powerful.